STAM11 Probability Theory

This course gives a solid background in and understanding of the basic results and methods in probability theory at an advanced level. It deals with random variables in one and several dimensions, conditional distributions, moment generating functions and characteristic functions, multivariate normal distributions, quadratic forms, order statistics, convergence criteria for random variables, the Borel-Cantelli lemmas, convergence via transforms, the central limit theorem and strong law of large numbers. Also studied are Poisson processes; conditioning on the number of occurrences or on occurrence times, thinning of Poisson process and the compound Poisson process.